When betrothing a woman, the groom says "Behold, you are betrothed to me with this ring, according to the tradition of Moshe and Israel."

As explained in that article, "according to the tradition of Moshe and Israel" means according to the Torah. (See Tosfot Ketubot 3A dh Adata.)

As Rabbi Maurice Lamm puts it, Jewish marriage ... must follow the process ordained by "the laws of Moses," which he received on Mount Sinai, and "of Israel," the Oral Law as developed by the teachers in the Talmud, Codes, and Responsa.

If "Moshe" refers to Biblical Law, and "Israel" refers to Rabbinical Law, so why not say so explicitly? What is the significance of 'Moshe' and 'Israel'?

see Kerem Shloma siman 26. It gives Bais Din the right to annul the marriage retroactively if necessary.
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samAug 13 '12 at 2:08

see Tosfos gitten 33a ואפקעינהו ,which brings a interesting case which the Rabbanan can uproot the kiddusin and the mamzer will become pure and the women would be patur only if done without intention see it inside for more details.
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samAug 13 '12 at 2:44

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@sam: But the same thing could be said by saying "...according to Torah Law" or "...according to the will of the Rabbis". Why specify Moshe and Yisrael?
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MenachemAug 13 '12 at 3:10

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One answer, which is more homiletic than halachic, is that the groom is saying that the couple is married "like Moses and Israel" i.e. the relationship is that of Moses to the Jewish people.

Throughout the Chumash, the Israelites give Moses a hard time. Every time he turns around they're either clamoring to go back to Egypt or worshipping idols. For his part, Moses has a had time putting up with them (see Deuteronomy 1:12 and 9:7 for examples), yet whenever God threatens to destroy the Jews Moses still goes to bat for them. That is the relationship "like Moses and Israel", that whatever goes on between the couple they are still inseparable.